Robust observer–controller compensator design using the loop shaping design procedure and the algebraic method

This paper investigates robust observer‐controller compensator design using Vidyasagar's structure (VS). VS has a unit matrix parameter H similar to the Q parameter for the Youla–Kucera parameterization. VS can be designed based on the left coprimeness of the central controller in the H_∞‐loop shaping design procedure (H_∞‐LSDP) and therefore can preserve the intrinsic properties of the H_∞‐LSDP. This paper introduces algebraic methods to simplify the design of H in the VS controller by solving specific algebraic equations. In particular, the algebraic design of H can achieve two things. First, a dynamic H adjusts the tracking performance and yields the integral action. Second, a dynamic H rejects the input and output sinusoidal disturbances with known frequencies. These attributes are indications of the flexibility of the proposed method since the output‐feedback controller design of the H_∞‐LSDP cannot easily deal with such conditions. This paper discusses the achieved loop and the closed‐loop behavior of the system with VS, and also gives two numerical examples. The first example shows that the proposed method results in a better design in many aspects than the resulting from H_∞‐LSDP. The second example shows the application of the proposed method to rejecting input and output step disturbances, and input and output multiple sinusoidal disturbances, for which the H_∞‐LSDP can hardly be used. Copyright © 2009 John Wiley & Sons, Ltd.     

Delay distribution based robust H∞ control of networked control systems with uncertainties

Network induced delay in networked control systems (NCS) is inherently non‐uniformly distributed and behaves with multifractal nature. However, such network characteristics have not been well considered in NCS analysis and synthesis. Making use of the information of the statistical distribution of NCS network induced delay, a delay distribution based stochastic model is adopted to link Quality‐of‐Control and network Quality‐of‐Service for NCS with uncertainties. From this model together with a tighter bounding technology for cross terms, H_∞ NCS analysis is carried out with significantly improved stability results. Furthermore, a memoryless H_∞ controller is designed to stabilize the NCS and to achieve the prescribed disturbance attenuation level. Numerical examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

TRUST BY ASSOCIATION: A META‐REPUTATION SYSTEM FOR PEER‐TO‐PEER NETWORKS

Trust mechanisms are used in peer‐to‐peer (P2P) networks to help well‐behaving peers find other well‐behaving peers with which to trade. Unfortunately, these trust mechanisms often do little to keep badly behaving peers from entering and taking advantage of the network, which makes the resulting network difficult or impossible to use for legitimate purposes such as e‐commerce. We propose trust by association, a way of tying peers together in invitation‐only P2P networks in such a way as to encourage the removal of badly behaving peers. We use invitations to create a structure within the otherwise ad hoc P2P network. Using this structure, we create a meta‐reputation system where we measure a peer’s trustworthiness not only by its own behavior, but also by the behavior of the peers it has invited to join. The connection created between the peers takes advantage of the external social relationship that must exist before a peer can be invited into the network. The result is a P2P network where, rather than just trying to marginalize badly behaving peers, there is incentive to kick them out of the network. We present results from a simple simulation showing that our approach works well in general when combined with and compared to an existing trust mechanism.     

Global existence and nonexistence for degenerate parabolic equations with nonlinear boundary flux

In this paper, by constructing various kinds of sub- and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions of global existence for nonnegative solutions to a degenerate parabolic system with completely coupled boundary conditions, which generalize the recent results of, for instance, Cui [Z. Cui, Critical curves of the non-Newtonian polytropic filtration equations coupled with nonlinear boundary conditions, Nonlinear Anal. 68 (2008) 3201–3208], Zhou–Mu [J. Zhou, C. Mu, Algebraic criteria for global existence or blow-up for a boundary coupled system of nonlinear diffusion equations, Appl. Anal. 86 (2007) 1185–1197] etc.     

On a new class of analytic functions associated with conic domain

The aim of this paper is to generalize the conic domain defined by Kanas and Wisniowska, and define the class of functions which map the open unit disk E onto this generalized conic domain. A brief comparison between these conic domains is the main motivation of this paper. A correction is made in selecting the range interval of order of conic domain.     

Step sequence planning for a biped robot by means of a cylindrical shape model and a high-resolution 2.5D map

A novel step sequence planning (SSP) method for biped-walking robots is presented. The method adopts a free space representation custom-designed for efficient biped robot motion planning. The method rests upon the approximation of the robot shape by a set of 3D cylindrical solids. This feature allows efficient determination of feasible paths in a 2.5D map, comprising stepping over obstacles and stair climbing. A SSP algorithm based on A^∗-search is proposed which uses the advantages of the aforementioned environment representation. The efficiency of the proposed approach is evaluated by a series of simulations performed for eight walking scenarios.     

A comparative runtime analysis of heuristic algorithms for satisfiability problems

The satisfiability problem is a basic core NP-complete problem. In recent years, a lot of heuristic algorithms have been developed to solve this problem, and many experiments have evaluated and compared the performance of different heuristic algorithms. However, rigorous theoretical analysis and comparison are rare. This paper analyzes and compares the expected runtime of three basic heuristic algorithms: RandomWalk, (1+1) EA, and hybrid algorithm. The runtime analysis of these heuristic algorithms on two 2-SAT instances shows that the expected runtime of these heuristic algorithms can be exponential time or polynomial time. Furthermore, these heuristic algorithms have their own advantages and disadvantages in solving different SAT instances. It also demonstrates that the expected runtime upper bound of RandomWalk on arbitrary k-SAT (k?3) is O(n(k−1)), and presents a k-SAT instance that has Θ(n(k−1)) expected runtime bound.     

Multi-frequency disturbance rejection via blending control technique for hard disk drives

This paper is concerned with the rejection of multiple narrowband disturbances in hard disk drives (HDDs). Inspired by a control blending idea, the multi-frequency disturbance rejection is formulated as a blending control problem. Each disturbance rejection is accomplished by using the H₂ optimal control method. Based on all H₂ optimal controllers, the blending technique is applied to yield a single controller which is capable of achieving rejection of all disturbances. Rejections of two and three disturbances for a 1.8-inch HDD VCM actuator are taken as application examples in the paper. Simulation and experimental results show that the ultimate controller results in a simultaneous attenuation of disturbances with frequencies higher or lower than the closed-loop system bandwidth. Moreover, the method turns out to be able to lift phase and thus prevent phase margin loss when it is used to deal with disturbances near bandwidth.